Question

The list shows the number of minutes that eight students spent on math homework last week. 22, 14, 24, 20, 36, 28, 43, 35What is the mean absolute deviation of the numbers

Answer 1

Given:

The data values are:

22, 14, 24, 20, 36, 28, 43, 35

To find:

The mean absolute deviation of the given numbers.

Solution:

We have,

22, 14, 24, 20, 36, 28, 43, 35

The measure of the given numbers is:

$\overline{x}=\dfrac{\sum_{i=1}^{n} x_i}{n}$

Where, $x_i$ represents the observations and n is the number of observation.

So, the mean value of the given data set is:

$\overline{x}=\dfrac{22+14+24+20+36+28+43+35}{8}$

$\overline{x}=\dfrac{222}{8}$

$\overline{x}=27.75$

The formula for is mean absolute deviation is:

$M.A.D.=\dfrac{1}{n}\sum_{i=1}^{n}|x_i-\overline{x}|$

The mean absolute deviation of the given numbers is:

$M.A.D.=\dfrac{1}{8}[|22-27.75|+|14-27.75|+|24-27.75|+|20-27.75|+|36-27.75|+|28-27.75|+|43-27.75|+|35-27.75|]$

$M.A.D.=\dfrac{1}{8}[5.75+13.75+3.75+7.75+8.25+0.25+15.25+7.25]$

$M.A.D.=\dfrac{1}{8}[62]$

$M.A.D.=7.75$

Therefore, the mean absolute deviation of the given numbers is 7.75.